SGPGI Nursing Officer-2023
Non Nursing Subjects
Medium
The perimeter of one face of a cube is 20 cm. Find the volume of the cube?
Appeared in: SGPGI Nursing Officer-2023
Explanation
- The perimeter of one face of the cube is given as 20 cm. Since a cube's face is a square, its perimeter is 4 times its side length (a).
- By setting 4a = 20 cm, we can calculate the side length 'a' to be 20 / 4 = 5 cm.
- The volume of a cube is calculated by cubing its side length (Volume = a³).
- Substituting the side length, the volume is 5³ = 5 × 5 × 5 = 125 cm³.
Why Other Options Were Wrong
- Option A: This value is incorrect. It may arise from a calculation error, such as incorrectly multiplying the perimeter (20) by the side length (5) and adding the side length again (20*5+20=120), which is not the correct formula for volume.
- Option C: This is an incorrect calculation. It does not correspond to the correct formula for the volume of a cube based on the given perimeter.
- Option D: This is an incorrect calculation. It might result from a simple arithmetic mistake when trying to compute 5³.
Related Visual
Clinical Relevance
- Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the volume of a cube from the perimeter of one of its faces as background academic context rather than a clinical decision trigger.
- While not a direct clinical scenario, this question tests fundamental mathematical and logical reasoning skills essential for nurses.
- Nurses frequently use basic math for tasks like calculating medication dosages, IV drip rates, and patient intake/output, where accuracy is critical for patient safety.
- What if? If the question gave the total surface area as 150 cm² instead of the face perimeter, you would first find the area of one face (150 / 6 = 25 cm²), then the side length (√25 = 5 cm), leading to the same volume (5³ = 125 cm³).
How to Approach the Question
- Identify the given information: The perimeter of one face of a cube is 20 cm.
- Recall the properties of a cube. A cube has square faces, and the perimeter of a square is 4 times its side length (a).
- Use the given perimeter to calculate the side length of the cube: 4a = 20 cm, so a = 5 cm.
- Recall the formula for the volume of a cube: Volume = a³.
- Substitute the calculated side length into the volume formula: Volume = 5³ = 125 cm³.
- Compare the result with the given options to find the correct answer.
Concept Tested & Keywords
- Concept Tested: Calculating the volume of a cube from the perimeter of one of its faces.
- Stem keywords: perimeter, face, cube, volume
- Lead-in keywords: Find
Question ID
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